Answer :
To find the probability of 5 cars waiting in line, we need to follow these steps:
1. Calculate the total frequency of all cars:
The given data shows the number of cars waiting at the bank and their respective frequencies over a 60-minute period.
[tex]\[ \text{Total frequency} = 2 + 9 + 16 + 12 + 8 + 6 + 4 + 2 + 1 \][/tex]
2. Identify the frequency of 5 cars waiting:
From the table, the frequency of 5 cars waiting is 6.
3. Calculate the probability:
The probability of an event is the ratio of the frequency of the event to the total frequency of all events.
[tex]\[ P(5 \text{ cars}) = \frac{\text{Frequency of 5 cars}}{\text{Total frequency}} \][/tex]
4. Substitute the values:
Using the calculated total frequency and the given frequency:
[tex]\[ \text{Total frequency} = 60 \][/tex]
[tex]\[ \text{Frequency of 5 cars} = 6 \][/tex]
[tex]\[ P(5 \text{ cars}) = \frac{6}{60} \][/tex]
5. Simplify the fraction:
[tex]\[ P(5 \text{ cars}) = \frac{6}{60} = 0.1 \][/tex]
Thus, the probability of 5 cars waiting in line is
[tex]\[ P(5) = 0.1 \][/tex]
1. Calculate the total frequency of all cars:
The given data shows the number of cars waiting at the bank and their respective frequencies over a 60-minute period.
[tex]\[ \text{Total frequency} = 2 + 9 + 16 + 12 + 8 + 6 + 4 + 2 + 1 \][/tex]
2. Identify the frequency of 5 cars waiting:
From the table, the frequency of 5 cars waiting is 6.
3. Calculate the probability:
The probability of an event is the ratio of the frequency of the event to the total frequency of all events.
[tex]\[ P(5 \text{ cars}) = \frac{\text{Frequency of 5 cars}}{\text{Total frequency}} \][/tex]
4. Substitute the values:
Using the calculated total frequency and the given frequency:
[tex]\[ \text{Total frequency} = 60 \][/tex]
[tex]\[ \text{Frequency of 5 cars} = 6 \][/tex]
[tex]\[ P(5 \text{ cars}) = \frac{6}{60} \][/tex]
5. Simplify the fraction:
[tex]\[ P(5 \text{ cars}) = \frac{6}{60} = 0.1 \][/tex]
Thus, the probability of 5 cars waiting in line is
[tex]\[ P(5) = 0.1 \][/tex]
